This is not a big deal. Just curious.
A trapezoid has an area of 108 m2. Base 1 is 12 meters and base 2 is 15 meters. What is the height?
Sixth grade for my DD, though the curriculum has changed since then so not sure if that is still where it would be covered.
CCSS puts it at 6th grade. Specifically:
CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
I agree that finding the area of a trapezoid seems to be 6th grade material by current standards, but what about the algebra needed for this one?
They do a lot of algebra before the subject called algebra.
For my DD, this type of problem was not unusual. I believe our math curriculum used this type of thinking fairly early on, though personally I don't think I would consider it to be learning algebra.
I actually have strong memories of the trapezoid/parallelogram/rhombus unit because it was a particularly good one, where DD worked in a small group where they were asked to derive the formulas, based on what they had learned about other shapes. She loved it, and still talks about it.
I'm not very mathy, I admit. I also have not been paying much attention to the math book! But to solve that problem, you solve for x, and it's not, you know, 2x =10. If that isn't algebra, what is it? (BTW, my DD could do it, but AFAIK she's still quite a ways away from "algebra," depending on what math course she tests into.)
I guess I don't know, but perhaps it's semantics, or maybe it's just me. Don't kids in early elementary often solve for unknowns using manipulatives and such? I know some people get excited that their second grader is doing algebra, I guess I sort of reserve that term for the actual course, while of course the concepts and groundwork may begin much earlier.
Well, I don't consider it algebra when my 1st grader answers x + 1 = 10, although it's intended to lay the groundwork, just as you say. I'd consider solving 108 = 1/2h(27) to be different, though you could do it by trial and error. However, my DD did it the traditional way. It doesn't really matter. I was just curious because I didn't expect this in her current course and wondered if it was a Common Core change.
DD did this sort of thing sometime between 4th and 6th grade.
Common Core, however, is now tethering it as a 6th grade skill.
For instance, IXL considers 2w – 5 = 3 to be a grade 8 algebra problem. ??
Ah, but CC does say: "Reason about and solve one-variable equations and inequalities" for 6th grade
I think that's anchored to the sixth grade standard:
CCSS.MATH.CONTENT.6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q
and x are all nonnegative rational numbers.
5th grade "GT" math which is supposed to be 6th grade "regular" math. That was the case pre-CC as my oldest covered it 8+ years ago. I wouldn't place too much faith in commercial online programs - in my limited experience, many of these programs are not as high level as they claim.
DD is in 5th grade GT math, so this appears to be appropriate. I was curious because I certainly do not remember solving equations like this at this age, though a straight-ahead area problem (find area of various shapes with standard measurements given) would have been on the agenda. I'm pretty rusty on how these things are sequenced.
I just showed it to DD10 who did said that she learned how to do this during the AOPS Pre-Algebra class which she took last year. Knowing how to do this by the end of 6th grade sounds about right given that the AoPS class describes itself ( or used to before Common Core) as an adequate 6th curriculum.
I've seen that sort of problem in the Singapore math books somewhere before the 6th grade level (though I'm not sure if it was with a trapezoid). I've definitely seen problems like that (with trapezoids) in various geometry books.
Interestingly, my DD was using an online application called First in Math in 1st and 2nd grade through her school. It was pretty good because the 'higher stuff' was open too - it held her attention until she found that 'Grand Master' was as high as one could go LOL
By the end of the second term of 2nd grade she had completed the 4th grade stuff there. One of the area and perimeter exercises involved working out the lengths of the sides of a rectangle with a perimeter of say x and an area of say y. I was impressed because pretty well the same reasoning lies behind the factorization of simple quadratics.
The school stopped that and we discovered AoPS but I have to say my DD enjoyed that app for a while. It really helped her with her fluency and mental arithmetic too.
The formula for a trapezoid, if you understand the angles don't matter, is very easy to derive visually. Like in a cut and paste common core number sense kind of way. If it's symmetrical you fit the left triangle into the space above the right triangle and get a rectangle that is the length of the short side plus another rectangle that's half the difference in the lengths. The area of this trapezoid is the same as any other one with the same bases, so it doesn't really have to be algebra at all. It's like starter geometry. I don't remember the formulas from school and just thought about the idea and then double checked with Google that I know what a trapezoid was. It looks harder than it is, until you draw it.